Composite sequence filter for current circuits



Jan. 18, 1949. w. K. soNNEMANN 2,459,596

COMPOSITE SEQUENCE-FILTERS FOR CURRENT-'CIRCUITS Filed April 4, 1947 CT C rb 3 310 7 7 140' -Aw j x :160' 1.10.

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ATTORNEY Patented Jan. 18, 1949 COMPOSITE SEQUENCE FILTER FOR CURRENT CIRCUITS William K. Sonnemanm Roselle Park, N. J., as-

signor to Westinghouse Electric Corporation, East Pittsburgh, Pa., a corporation of lPenn- Sylvania- Application April 4, 1947, .Serial No. 739,469

4 Claims.

My invention relates to av single l sequencesegregating network having a, response which is controllably proportional, with any 'desired constants, to any two, or all three, of the positive, negative, and zero-sequence components of a three-phase current.

.An object of my .invention is to provide an improved network of the 'type just described, which .is somewhat more flexible in design, than previously known networks, and which utilizes impedance-elements which make ya more 4eillcient use of material and mounting-space.

My invention is an improvement over the sequence-networks which are shown on pages lM8 and '249 of the Electrical Transmission and YDistribution Reference Book, 1942 edition; Va Harder Patent 2,183,646, granted December 19, l1939; and my previously filed copending application Serial No. 591,079, filed April 30, 1945, for Controlsystems.

Composite sequence-segregating networks, or networks which respond, vin ldifferent magnitudes, to a plurality of different phase-sequence components of the input-current., are useful in relaying-systems or control-systems which are intended to respond to a plurality of different kinds of' faults, which may affect di-erent phases or combinations of phases of the impressed linecurrent. Thus, the Harder patent showed .a composite network vhaving -a heavily weighted respense to the zero-sequence current-component, and having a relatively small response to the positive-.sequence component, without any response to .the negative-sequence component.v Qn .the other hand, my previously mentioned copending application showed a network having a strongly Weighted negativesequence response, and a smaller positive-sequence response, `either with `a strongly weighted zero-sequence response or no zero-sequence response at all.

An object of my present invention is to provide a network which is capable of obtaining the foregoing and `other lcombinations lof responses, fand 'of doingso without'.l requiring .a three-winding reactor;

With the foregoing and other objects in view, my invention consists 1in the circuits, systems, combinations, apparatus, parts, and designthe accompanying drawing,

2 native forms of Vthe network, involving variations in the circuits, and

Figs. 4 and 5 are illustrative curve-diagrams which will be referred to in the subsequent description.

My novel sequence-filter network, as shown in Fig'. l, comprises four input-terminals T1, T2, Ts and To, two output-terminals F1 and F2, and three impedances Z1, Z2 and Z3. The rst three input-terminals, .'Il1,'T2 and T3, are supplied with a three-.phase system .of currents la, Ib, c or Ie, Ic, Ib. any event, the phase-of the 'current which iis .fed in through the 4iirst terminal, T1, is called phasea, and the other Vtwo phasesv are supplied to the other two phase-terminals T2 and T3, in either ,phase-sequence according to the selective sequence-.responses which are desired of the network. VThe last input-terminal To provides a return-path for the neutral-current 310 of a system of star-connected line-currents Ina, Ib, In. The three filter-impedances Z1, Znz and Z3 are respectively connected .between the 4terminals T1 and T2, T2 .and T3, and Ta and To, as shown in Fig. l. The two Ioutput-terminals Fi and F2 of the lteras shown in Fig.. 1 `are connected respectively to. the rst and. last input-r terminals T1v Yand To, or, vin general, `so as to be responsive to :the vectorial sum of` the voltagedrops in the three impedaneesZiffZz and Za.

vAs a consequence ofthese connections in Fig. 1, the impedance 'Z1=('r1+vix1) ='Z1 1 is trav; ersed by the current Ia; the impedance Z2=(m+7'2) =Z22 is traversed bythe current (Javi-Ie) or (Imi-Je). .according .to the phasesequence of the input-connections; zand the impedance Zz=n+1ix3 =zz is traversed by the zero-sequence current-'componentsloz la+a+1ar The no-load voutput-voltage Vr of the lter of Fig. 1 is ci VF i..z1-+ can; 2431.23

(2) V;=,+B,+C'T0 where the r'coefficients of' thelter-'responses tothe positive, negative and zero phase-sequence current-components: '11, Iz and I0 are respectively,

In Equations 3 and 4, the rst of the alternative polaritiesof x/ applies when the second supplyphase is b, and the second polarity applies when the second supply-phase is c.

In accordance with my invention, the three impedances Z2 and Z's are given any magnitudes Z1, Za, Zr` and any phase-angles 1p1, qu, as which are necessary to provide (within limits) the desired sequence-responses A, B and C. In general, my present lter is designed to flexibly or adjustably provide a composite lter-response; that is, a response which is proportional, with different and controllable coefcients A, B and C. to any two, or al1 three, of the positive, negative and zero phase-sequence components I1, I2 and Io of a polyphase current Ia, Ib, Ic.

In my lter-impedances Z1, Z2 and Z3, as shown in Fig. 1, the resistance-parts r1', rz and r3 ofthe impedances are necessarily positive, unless auxiliary insulating-transformers of current-transformers` are used, to reverse the direction of current-now through one or more of the impedances, such as Z2 and Za. as indicated, by way of example, at C'Iz and CTB in Fig. 3. When this is done, my filter-network may be made to respond to a single one of the rotational phase-sequence compoentsi that is, to either the positive-sequence component I1, or the negative-sequence component z, as may be desired.

In general, however, the auxiliary currenttransformers CIz and CT3 of Fig. 3 are not used, and hence the zero-sequence network-response C will not 'be zero, because (r1-l-2r2-l-3ra) will always have a nlte positive value, in Equation 5.

The three reactance-components x1, :c2 and :r3 of the network-impedances Z1. Z2 and Za in Fig. l. may have either positive values, representing inductors or mutual-inductance couplings, or negative values, representing capacitors. As shown in Fig. 2, two-coil mutual-inductance transformers M1 and M3 may be used, for, or in, either or both of the end-connected impedances Z1 and Z3; and the secondary or output-circuit windings of these two-coil reactors', M1 and M3 may be connected in the output-circuit of VF in either polarity, to provide either positive or negative values oi :c1 and ma, respectively. The mutual reactors M1 and M3, and the self-inductance coil m2, in Fig. 2, have airgap iron cores 4. In general, this method of providing negative values of the reactancecomponents :r1 and 1:3 is preferable tousing capacitors. The middle reactance-component z2 does not generally need to be negative, because the desiredresponse-characteristics can usually be obtained by assigning proper values to :c1 and ma to correspond to a zero or positive value of z2; but if a negative value of :c2 is desired, it can best be obtained by using an auxiliary, reverseconnected, current-transformer CTz, as shown in Fig. 3.

.It will be noted, from Equations 3 and 4, that the third filter-impedance, Z3, does not affect the positive and negative responses A and B. Let us .first examine, therefore, the relations between the lter-impedances Z1 andZ-z, and the positive and negative phase-sequence responses A and B in Equations 3 and 4. The zero-sequence response in Equation 5, may then be given any magnitude C or phase-angle oc, by assigning proper values to the third impedance Z3= r3lia The ratio k of the magnitudes of the negative and positive phase-sequence responses B and A is a positive number which is given'by the equation,

In Equation 8, there are really only three variables. There is the ratio .e of the magnitude Z2 of the second impedance to the magnitude Z1 of the rst impedance. This is a positive number, given by the equation,

Then there is an angle (1p1-o2) by which the iinpedance-angle qu of the first impedance Z1 leads the impedance-angle o2 of the second impedance Z2. This gives us a variable, which is defined by the two equations,

And nally there is a variable K, which is dependent upon the negative and positive responseratio 1c which is dened in Equation 6. The variable K is dened by the equation,

zg m@ The conditions for no response to the positivesequence component, and for no response to the negative-sequence component, are, respectively, (17) k= 01 o izil..

audace ot" the conditions stated: in (17B) and (1WD). are'valld. That is, or may equal either (if-iiwfiorner-120i) with the two impeda'nces zi and. 'Zr equal to each other in absolute magnitride. In eitherA event, either the negativesequen'ce response-characteristic Bor the positive-sequence response-characteristic A will be zero, depending 'upon' Whether thesecond supplyphas'e, of' terminal T2, is b orl c. If an auxiliary current-transformer GT2 (Fig. 3) is to be avoided, it is usually desirable to use the relation iigepz) :ef-120 in Equation 17D, making p2 positive; and' qirne'g'ati've. However, if" the zeroseduence res'ponse-characteristic C is to be made zero, an auxiliary current-transformer will be necessary,V anyway, as shown at CT2 or C'Is in Fig. 3, for supplying current to either all, or a part of,.the` impedance Z2 or Z3, so as to produce the eect of a negative resistance r2 or r3, and in such a case, (4u-qm). might as well be +120 as -120. Two illustrations will suice.

according as the second supply-:phase is b or c. If the proper values are assigned to the constants. Fig.' 2 will depict such a network. If the zeroseque'n'ce coefiici'ent. C is to be made Zero, an auxiliary current-transformer GT3 may be added, as shown in Fig. 3, toobtain by an angle (oA- 1113) which is given by the equation.

6 In designing a network toV have any required ratio Ic. between the negative-sequence responsecoefficient B and the positive-sequence response coefficient A, it is necessary, rst, to calculate K from the required value of k=B/A, according to Equation 12 which states that Itis then necessary to choose an arbitrary valueof the impedance-ratio z=Z2/Z1, which can have any positive value between the limits expressed in Equations 15 and 16, these limits being different foreach value of K2. It is then necessary to substitute the values of K2 and .e in Equation 14, which will show the impedance-angle-difference (.1-2)=cos1:c, which is necessary to produce the required negative-to-positive sequenceratio k when using the chosen value of the impedance-ratio z.

Twoillustrative examples are graphically plottedy in Fig. 5, in curves .r4 and mi, for the values K2=L28 and K'-=l.06, respectively. When K2=1'.28, Equation 12 shows that the sequenceratio lk is either 4.03 or 1/4.03; and when K2=1.06, 1c will be either 6.86 or 1/6.86. Whether k is greater or less than unity depends upon whether the second supply-phase is b or c, and whether the impedance-angle-difference 1-2 is positive or negative. Fig. 5 is plotted for negative values of (o1-o2), or positive values of (2-r),.

that is, for the case when the impedance-angle gsi of the rst impedance Z1 is more negative than (or leads) the impedance-angle o2 of the second impedance Z2. When the second supplyphase of the network is b, the conditions shown by the curves r4 and an in Fig. 5 will produce a quence-ratio k would be changed to 4.03 and 1c=1/6.86, respectively, meaning that the positive-sequence response-coeiiicient A is larger than the negative-sequence response-coefilcient B. If the second supply-phase were changed from o to c, or if the impedance-angle-diference (oz-(7n) were changed from positive to negative, the sequence-ratio k would be changed to 4.03 and 6.86, respectively, that is, B would he larger than A; but if both the phase-sequence of the supplyconnections and the sign or polarity of the impedance-angle-diference (rpo-gti) were changed,4 Fig. 5 would still represent the design-conditions for k=1/4.03 and 7c=1/6.86, in curves :r4 and srv, respectively.`

From Fig. 5 and Equation 14, it will be noted that the maximum and minimum values of i(1-i2)=cos`1a: will be obtained when the impedance-ratio 2:1, that is when Zi=Z2. In such a CS'e,

eis/Muere In curve r4, with K2`="1.28 in Fig. 5, the limiting values of (oz-1p1) are approximately 141.65 and 92.42., lrespectively; whereas, in curve xv, with Kit-11.06, tlre limiting values of (c2-e1) are approximately 131;'3" 'and 10723", respectively.

Eig.; f5 andi Equations i5 and 16 show that the maxirrrum and minimum possible values of the impedance-'ratio ezZe/Zi 'for H2L-1.281. in curve an; Iazreapproxhnately 1.558 and 0.6417, respectively; whereas, `for K2=1.06, in curve .17, the irnpedance-ratio e must lie Within the limits, 211.234 and 2.20.8101, or 22:1234' Z1 and 532:0.8101 Zi., approximately.

7 be various values of the phase-angle-'difference (eA-e) between the phase-angles of thel positiveand negative-sequence response-coefficients and B, as shown in Equation 21, which emresses the value of T=tan (oA-es). This variation is illustrated in Fig. 4, in the curves T4 and Tf1, which correspond, respectively, to the curves :c4 and xv in Fig. 5, for the values, K2=1.28 and K2=l.06, respectively. Whatever may be the value of K, the angle-difference (eA-(ps) between the positiveand negative-sequence coeicients .A and will always be --120 or 605, when z=1, that is, when the absolute magnitudes Z1 and Z2 of the rst two network-impedances Z1 and Z2 are equal. When s has its maximum value 1.558, when K2=1.28, in curve T4, (eA- 1513): approximately -l36.67, and when .e has its minimum value 0.6417, when K2=l.28, in the same curve, (qm-qm) :approximately +164". When K2=1.06, as in curve T7 in Fig. 4, (oA-fps) :approximately -143.1 when e has its maximum value 1.234, and (QSA-es) :approximately +23.0 when e has its minimum value 0.8101. By choosing different values of .e between its maximum and minimum limiting-values, the phase-diierence (oA-(ps) between the positive-sequence and negative-sequence response-coeflcients may be given any value between 0 and 360.

It should be noted that Equation 2l yields four alternative values of (qbA-rp) =tan-1T, for each pair of values of K and a. Which one of these four alternative values is applicable must be determined by substituting each pair of Values of K and e in Equations 3 and 4, wherein using the top sign of the radical \/3r when the second supply-phase is b, and the bottom sign when the second supply-phase is c. Both the sine and cosine of each angle must be calculated, in order to determine which quadrant the angle is in.

In Fig. 4, it may be noted that changing the sign or polarity of (1--2) without changing its magnitude, makes no difference in (QSA-en); but changing the phase-sequence of the input-currents, that is, changing the second supply-phase from b to c or vice versa, changes the sign or polarity, but not the magnitude, of (oA-45B) In all of the forms of embodiment of my invention, whether the positive-sequence response is large, small, or zero, or whether the negative'- sequence is large, small, or zero, the Zero-sequence response may be given any Value at all, whatever may be desired, whether large, small, or zero, and having any phase-angle 41D with respect to the positiveor negative-sequence phase-angle on or 95B, by assigning appropriate values to the resistance r3 and the reactance :1:3 which make up the impedance Z3 in Figs. 1, 2 or 3. The zerosequence response-coefficient C is as shown in Equation 5. In using this equation, it is necessary to insert the specific values of r1, r2, :1:1 andata which are determined by therequired relations between the positiveand negative-sequence response-characteristics, Ic=B/A and (eA-96B), as has been described in detail. The proper values of 1s and x3 may then readily be determined for giving the zero-sequence response-characteristic C any desired magnitude and phase-angle, in Equation 5.

While I have described the general principles ofv my invention, and have illustrated the same with a few chosen examples, it is to be understood that my invention is not limited, of course, to the specific and illustrative examples which have been chosen. I desire, therefore, that the appended claims shall be accorded the broadest construction consistent with their language.

I claim as my invention:

l. A sequence-segregating current-network comprising four input-terminals for a threephase current and a return-current conductor, respectively, two output-terminals, three separate impedances having substantially no mutual reactance therebetween, supply-circuit means associated with the rst and second input-terminals for causing one of said impedances to be traversed by an input-current of one phase, supply-circuit means associated with the second and third input-terminals for causing another impedance to be traversed by the sum of that phase and one of the other phases of the input-current, supply-circuit means associated with the third and fourth input-terminals for causing the third impedance to be traversed by the return-current, and output-circuit means associated with the three impedances for causing the two output-terminals to be supplied with the sum of the voltage-drops in the three impedances.

2. A composite sequence-segregating currentnetwork as defined in claim 1, in which the three impedances have such values as to produce an output-voltage which is responsive to a plurality of the phase-sequence components of the threephase input-current.

3. A network as defined in claim 1, characterized by the three impedances having the values Z1=Zi1=T1-i-jl*1,Zz=Z22=T2li32a and Z3=Z3 a=rs+j:rs, respectively, in which the ratio, e=Z2/Z1, of the rst two impedances, and the phase-angle-difference, (gn-112) =cos 1:l:, between them, are related to each other, and to the desired network-constant, K=(k2+1)/(7c21), where k=B/A is the ratio between the magnitude of the desired negative-sequence response B and the magnitude of the desired positive-sequence response A, by the formula,

for any chosen value of z, chosen between certain limits, dened as ,www

and

4.... 4 2 Z@(324 i) 92K (6K +3) and the third impedance, Z3, has whatever value may be needed, with the values of Z1 and Zz thus obtained, to provide the desired zero-sequence response,

4. The invention as dened in claim 1, includ- REFERENCES CITED ing means for reversing the polarity of the volt' The following references are of record in the age-drop across a portion or all of one or more me of this patent. of the impedances lnoluded in the network.

v 5 UNITED STATES PATENTS WILLIAM K. SONNEMANN. Number Name Date 1,535,587 Evans Apr. 28, 1925 2,183,646 Harder Dec. 19, 1939 

